The divergence of a vector D for rectangular coordinate is equal to [1/p / dp (pDp)] + [1/p Dø/dø]+ [ƏDz/az]

Q: show that the function 3x³y-y²³ +y is ty h harmonic and then find it's Harmonic conjugate v (x, y)

A: The given problem is check the given function is harmonic or not and also to find the harmonic…

Q: Find the residues of f(z) = z²-2z (z+1)²(z²+4) at all its poles in the finite plane

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Q: x3+y3 x+y If u = = In ди X ?x In ( ди + у ду then find the value of ?

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Q: Solve the following by using In

A: 5. (i) Given,              s2s4-1

Q: Solve the problem. 1-3 0 11 -18 -4 02 Let A = and b = 3 -16 Define a transformation T: ³-> R³ by…

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Q: 13. How many license plates consisting of two letters followed by two number repetition is allowed?

A: To find: the number of number plates.

Q: d s: X = (0,1, -1) + λ (1, α, 2α) are coplanar, in which case study its relative position.

A: Consider the given lines. r: X=(1,0,2)+λ (2, 1, 3) And, s:X=(0,1, -1)+λ(1, α, 2α) Let r and s are…

Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost+to(t-2). (b)…

A: The Laplace transformation is very significant integral transformation that is used widely in many…

Q: The graph below is the function f(x) 3 02 -5 -4 -3 -2 -3- Determine which one of the following rules…

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Q: given that u = Solve the heat conduction equation д2и ди = 2x2 Әt 0, when t → ∞o, x = 0, x = 1.

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: Given the funciton: x2 − x + 6 / x - 6 a.) Identity the x-intercept and y-intercept.  b.) Find…

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Q: Express the given quantity in the form a + ib. cot(+71) 2

A: Given: cot π2+7i To find: Solution

Q: Here are two new definitions about graphs. The distance between two vertices in a graph is the…

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Q: II. SOLVING: Solve the given linear system using Gauss-Jordan elimination x₁ + 2x₂ + 2x3 - 2 = 0…

A: we can solve the given system of linear equations .

Q: State why the function 22²-37 +ě is analytic everywhere

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Q: Solve 2-D

A: Introduction:   A differential equation is an equation that contains the derivative of an unknown…

Q: Use telescopic method to solve the recurrence relation f(0) = 4 and f(n) = f(n − 1) + 2n − 1 for all…

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Q: 2 (x + 3π)]dx

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Q: 6. Find the Laplace transform of the following functions (a) g(t) = et+2+ sint cost+to(t-2). (b)…

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Q: Find the equation of the tangent plane to the graph of f(x, y) = 3xy² + 2x³y² at the point (-2, 3).…

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Q: show that the following function analytic f(z) = 4e²+ Sin Z arp

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Q: x yy' + 4x² + y² = 0 y(2)=-7, x > 0 This is homogeneous. Solve it using the method of homogeneous to…

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Q: For the primal and the associated dual problems shown below, use the complementary slackness theorem…

A: Given: x1 = 0 , x2 = 4/3 , x3 = 1 Maximize , -4x1-6x2-5x3  Subject to  2x1 +3x3 ≥3 3x2+2x3≥6x1,x2,x3…

Q: Let f(u, v) be a differentiable function with f(-1,3)=0, fu(-1,3)= 2 and f(-1,3)= -3, g(x, y, z) =…

A: Given that f(u, v) is a differentiable function with f-1,3=0, fu-1,3=2 and fv-1,3=-3,…

Q: Prove that if v>-1/2 H₂ {xv-1 e-ax; p} = L{xº J₁ (px); a} = 2Upr (v + 1/2) √√ (a² + p²)+1/2

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Q: Data on 30 grades of Statistics courses. 54 76 83 49 84 65 55 79 92 59 67 86 63 79 64 52 58 90 60 78…

A: a.)   Data from smallest to largest:495254555658585960626364656769727576787979798384858687909292

Q: Q1. Use reduction of order to find the second solution y₂ (x), if the indicated function is a…

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Q: Orange juice, a raisin bagel, and a cup of coffee from Billy's Breakfast Bar cost a total of $2.40.…

A: We have to (a) Find what was the cost of a glass of orange juice before the increase.  (b) Find what…

Q: S 00 -² dx = LEN π 2

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Q: In Mathematics one of the assessment methods is journals, by using an example explain this method…

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Q: mpounding interest and an APR of 4.5% in sume no additional deposits are made.

A: Given as, 8 years is $25,000 and APR of 4.5%.

Q: ind Laplace Transform of the expression. f(t) = e-5 H (t-2)

A: Sol Le-tHt-2 Apply transform rule:  if Lft=Fs then  Leatft=Fs-a

Q: A doll sold for $253 in 1975 and was sold again in 1986 for $408. Assume that the growth in the…

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Q: factor of the equation dy dx The Integrating (x²y³ + xy) 1 is

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Q: Use the power series method to solve the given initial-value problem. (Enter the first four nonzero…

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Q: 1. Let X and Y be non empty sets and let £: XY be given. Prove that if M is a algebra of subsets of…

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Q: 1. How many arrangements could be made of the word GRATEFUL if: o there are no restrictions? o the…

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Q: Find the volume of the solid generated when the plane region bounded by: y=e^(-x^2 )  and the…

A: The given problem is to find the volume of the solid generated when the given plane region in…

Q: The complete solution of the ordinary differential equation ď² y dy + P dx +qy = 0 is dx² - 3x - y =…

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Q: 5. Lena used 36 m of fe garden on her farm a) Sketch some pos What is the area. b) How many differ.

A: Given, The length of fencing is used to enclose a rectangular vegetable is 36 m.

Q: ensor analys

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Q: [(p^~q) v~r] ^ (q^r)

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Q: Q5. Solve the following by using Inverse Laplace Transform (i) s² S4-1 (ii) 3s-14 s²-7s+10

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Q: A restaurant purchased kitchen equipment on January​ 1, 2017. On January​ 1, 2019, the value of the…

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Q: y' − (4x − y + 1)² = 0 y(0)=2 -

A: To solve the given differential equation  y'-4x-y+12=0 with initial condition y0=2

Q: What is the MOST acceptable method to determine the general solution for the function? y" - y' - 2y…

A: We know that , method of undetermined coefficients used to find particular solution of…

Q: 12. Camy bought three types of fish. The bar graph shows the number of each type of fish Camy…

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Q: The simply supported beam loaded as shown. The length of the beam is 6 m, a = 4 m, the load P = 4000…

A: Given: l=6m, a=4m, P=4000N To find: Solution

Q: Let X be co or lº, 1 ≤ p ≤ ∞o. Consider the operator Prove that U is not compact but U² is compact.…

A: Please find the answer in next step

Q: Consider the following differential equation to be solved using a power series. y" + xy = 0 00 Using…

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